System and method of transmit beam selection

ABSTRACT

A system and method of beamforming facilitate beam selection without requiring an exhaustive search. In some implementations, a beamforming technique may select candidate vectors to construct a beamforming matrix without having to compute each matrix element.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of U.S. provisionalapplication Ser. No. 60/914,479, filed Apr. 27, 2007, entitled “TransmitBeam and Antenna Selection for MIMO Systems,” the disclosure of which isincorporated herein by reference in its entirety.

The present application is also related to co-owned U.S. patentapplication Ser. No. 12/044,117, filed Mar. 7, 2008, entitled “CodebookSelection Algorithm for Transmit Beamforming,” and U.S. patentapplication Ser. No. 12/062,462, filed Apr. 3, 2008, entitled “Systemand Method of Beamforming with Reduced Feedback,” the disclosures ofwhich are incorporated herein by reference in their entireties.

BACKGROUND

1. Field of the Invention

Aspects of the present invention relate generally to wirelesscommunication techniques, and more particularly to a system and methodof beamforming that select candidate vectors to construct a beamformingmatrix.

2. Description of Related Art

Recently, the wireless communication industry has demonstrated anincreasing interest in beamforming techniques for use in connection withmultiple input, multiple output (MIMO) systems. For example, MIMObeamforming systems have been considered in standards promulgated by theInstitute of Electrical and Electronics Engineers (IEEE), most notablythe IEEE 802.11n standard for wireless local area networks (WLANs). Oneadvantage of beamforming methodologies is that they can increase thedata rate between networked devices without the attendant increase intransmit power or bandwidth that would be necessary to achieve a similardata rate in MIMO systems without beamforming.

One relatively popular beamforming approach uses singular valuedecomposition (SVD) techniques. However, this method requires a lot offeedback information (i.e., signal information transmitted from thereceive device back to the beamforming transmit device). ConventionalSVD beamforming also introduces transmit power fluctuations amongantennae; thus, traditional beamforming strategies may not efficientlysatisfy a per-antenna transmit power constraint.

Therefore, it may be desirable in some instances to provide abeamforming technique that requires significantly less feedbackinformation than the SVD beamforming technique; additionally, it may bedesirable to provide a beamforming strategy that does not require anexhaustive search for every element of a beamforming matrix.

SUMMARY

Embodiments of the present invention overcome the above-mentioned andvarious other shortcomings of conventional technology, providing asystem and method of beamforming that facilitate beam selection withoutrequiring an exhaustive search. In some implementations, a beamformingtechnique may select candidate vectors to construct a beamforming matrixwithout having to compute each matrix element.

The foregoing and other aspects of various embodiments of the presentinvention will be apparent through examination of the following detaileddescription thereof in conjunction with the accompanying drawingfigures.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

FIGS. 1A and 1B are simplified diagrams illustrating components of atransmitter and a receiver employing embodiments of a system and methodof transmit beam selection.

FIG. 2 is a simplified flow diagram illustrating operation of oneembodiment of a beamforming method that selects candidate vectors toconstruct a beamforming matrix.

FIG. 3 is a simplified flow diagram illustrating operation of anotherembodiment of a beamforming method that selects candidate vectors toconstruct a beamforming matrix.

DETAILED DESCRIPTION Introduction

The beamforming techniques described below may be utilized for flatfading channels as well as for frequency selective fading channels withorthogonal frequency division multiplexing (OFDM). For simplicity, thebeamforming techniques are explained in the context of single carriersystems for flat fading channels; those of skill in the art willappreciate that the disclosed methodologies may readily be extended tobe implemented in OFDM systems.

In some implementations, the receive signal may be modeled asy=Hx+z  (Equation 1)y=[y₁ . . . y_(N) _(R) ]^(T)  (Equation 2)where

$\begin{matrix}{H = \begin{bmatrix}h_{1,1} & \ldots & h_{1,N_{T}} \\\vdots & \ddots & \vdots \\h_{N_{R},1} & \ldots & h_{N_{R},N_{T}}\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$x=[x₁ . . . x_(N) _(T) ]^(T)  (Equation 4)z=[z₁ . . . z_(N) _(R) ]^(T)  (Equation 5)

In this model, x_(t) is a transmit signal from a transmit antenna, t,z_(r) is the noise in a receive antenna, r, H is the instantaneouschannel matrix where h_(r,t) is a channel gain from transmitter, t, toreceiver, r, and N_(R) and N_(T) are the number of receive and transmitantennae, respectively. Additionally, N_(S) may represent the number oftransmit streams, which should be constrained such thatN_(S)≦min{N_(R),N_(T)}.

In many cases, the transmit signal vector, x, is generated by linearlyprocessing a data vector, d, with a transmit beamforming matrix, B:x=Bd  (Equation 6)where the data vector d isd=└d₁d₂ . . . d_(N) _(S) ┘^(T)  (Equation 7)

In Equation 7, d_(s) generally represents a data symbol for a stream, s,and N_(S) represents the number of streams, as noted above. The matrix Bspecifies how the data streams are mapped to the transmit antennae, andit can also be thought of as a beamforming matrix, each column of whichrepresents a transmit beam for a respective data stream.

It will be appreciated that receiver performance may be affected by themanner in which a transmit beamforming matrix, B, is selected.Accordingly, overall system data throughput and reliability may beinfluenced by appropriate selection of the transmit beamforming matrix.One conventional way of selecting a beamforming matrix generallyinvolves using singular value decomposition (SVD) on the channel, H.However, the SVD approach is usually computationally complex, and itrequires a significant amount of feedback in the case of explicitbeamforming. So, in practical situations, it may be desirable to providea beamforming scheme that minimizes or otherwise limits the number ofcandidate beams (or candidate vectors for the beamforming matrix) thatneed to be searched.

Turning now to the drawing figures, FIGS. 1A and 1B are simplifieddiagrams illustrating components of a transmitter and a receiveremploying embodiments of a system and method of transmit beam selection.In some embodiments, the functional blocks illustrated may beimplemented as hardware components. For example, the various elements ofreceiver 200 may be integrated into a single, monolithic integratedcircuit (IC) or an application specific IC (ASIC). Additionally oralternatively, some or all of the functional blocks may be implementedindependently (i.e., on multiple ICs or chips), for instance, usingprogrammable logic hardware or more than one ASIC. In someimplementations, various of the elements may be programmable orotherwise configurable in accordance with system requirements,communications protocols, and other factors affecting desired ornecessary operational characteristics of transmitter 100, receiver 200,or both. In that regard, some of the functional blocks of transmitter100 or receiver 200 may be implemented in software or other encodedinstruction sets, for example, executed by a microprocessor ormicrocontroller (not illustrated in the drawing figure). Accordingly,the term “module” in the context of the following description isintended to encompass both hardware and software embodiments of aparticular functional block; those of skill in the art will appreciatethat any number of software applications or instruction sets, andvarious circuitry or hardware components supported by firmware mayreadily be designed to support the functionality set forth below.

Transmitter 100 generally comprises a plurality of transmit antennas (X₁. . . X_(NT)). In some implementations, such as illustrated in FIG. 1A,a transmit vector generation module 110 may be configured and operativeto construct a transmit signal in accordance with a beamforming matrixsubstantially as set forth above with reference to Equations 6 and 7.Alternatively, where feedback from the beamformee is in the form of anindication as to which transmit antenna should be used as indicated inFIG. 1B, transmitter may include switch logic 111 or an equivalentmodule operative selectively to connect each input data symbol to one ofthe transmit antennas X₁ . . . X_(NT) exclusively, in accordance withthe feedback signal.

Similarly, individual Inverse Fast Fourier Transform (IFFT) modules 140and parallel to serial modules 150 may transform to the time domain andformat, respectively, each data stream for transmission. Followingaddition of a cyclic prefix at module 160, data streams (e.g., x₁, x₂,etc.) may be transmitted in a conventional manner. In that regard, thearchitecture of the FIG. 1 embodiment may have utility in systemsoperating in accordance with various communications protocols such as,but not limited to, IEEE 802.11n (WLAN) or Wireless Fidelity (WiFI)systems, Worldwide Interoperability for Microwave Access (WiMAX)systems, and various OFDM networks.

It is noted that transmitter 100 may generally comprise additionalcomponents not illustrated in FIGS. 1A and 1B. For example, transmitter100 may include a sounding signal generation module to construct asounding signal that allows a receiver to estimate the full-dimensionalMIMO channel, from which the beamforming matrix may be derived.Transmitter 100 may also include baseband modules, modulators, localoscillators or frequency references, and other components generallyknown in the art of wireless communications, such as, but not limitedto: Inverse Fast Fourier Transform (IFFT) modules and parallel to serialmodules operative to transform to the time domain and to format,respectively, each data stream for transmission. Transmitter 100 mayalso comprise an equalizer to perform equalization on the effectivechannel matrix substantially as set forth below; such an equalizer mayimplement any of various types of known equalization techniques. In someembodiments, transmitter 100 may also comprise a signal to noise ratiocalculation unit to calculate a respective signal to noise ratio foreach beam in the equalized effective channel matrix as set forth indetail below.

It will be appreciated that receiver 200 operative to communicate withtransmitter 100 may comprise modules that are similar to thoseimplemented at transmitter 100. For example, receiver 200 may comprise abeamforming matrix module 210 that is capable of performing thefunctionality described below for constructing, calculating, orotherwise selecting a beamforming matrix to be fed back to transmitter100. In that regard, receiver 200 may include a channel estimationmodule 211 to calculate a channel estimate from a transmit signalreceived from transmitter 100; such a channel estimate may have utilityin calculating a beamforming matrix. In some embodiments, thefunctionality of modules 210 and 211 may be integrated into a singlemodule, hardware component, or functional block; in particular, as setforth below, a beamforming matrix module 210 may be operative toconstruct an effective channel matrix, therefore performing thefunctionality illustrated as performed by module 211. In the embodimentof FIG. 1B, an antenna selection module 213 may feedback a signal totransmitter 100 indicating which transmit antenna to use as a functionof the channel estimate. As indicated in FIGS. 1A and 1B, receiver 200may also comprise an equalizer module 212; the functionality ofequalizer module 212 is set forth in detail below.

Additionally, receiver 200 may comprise suitable antenna and transmitterhardware, as well as appropriate serializer, de-serializer, andtransform modules enabling bi-directional data and other communications.As noted above with reference to transmitter 100, such modulesimplemented in receiver 200 may be embodied in hardware (such asdedicated circuitry, programmable logic, or ASIC hardware) or softwareapplications or instruction sets executed by a microprocessor ormicrocontroller. Further, components of receiver 200 may readily beimplemented in transmitter 100 in some embodiments. For example,beamforming matrix module 210 may be disposed in transmitter 100, andreceiver 200 may be configured to feedback the channel estimate, ratherthan the matrix, B, to transmitter 100. Similarly, both channelestimation module 211 and beamforming matrix module 210 may beimplemented at transmitter 100; in this case, the channel may be assumedto be reciprocal (i.e., the uplink channel is equivalent to the downlinkchannel). Similar variations may employ antenna selection module 213 atthe transmit side.

The architectures illustrated in FIGS. 1A and 1B may have utility insystems operating in accordance with various communications protocolssuch as, but not limited to, IEEE 802.11n (WLAN) or Wireless Fidelity(WiFI) systems, Worldwide Interoperability for Microwave Access (WiMAX)systems, and various OFDM networks. The architectures are provided byway of background only; it will be appreciated that the followingbeamforming protocol may be employed by the illustrated arrangements orother suitably configured architectures.

Implementation

In accordance with some embodiments, a transmit beamforming matrix, B,may be constructed by selecting N_(s) columns of a transmit beamcandidate matrix, C. The dimensions of the candidate matrix aregenerally N_(T)×N_(C) where N_(C) represents the total number ofcandidates. The transmit beam candidate matrix, C, is generally given(i.e., predetermined), and may vary in accordance with overall systemrequirements or design, such as transmit power constraints, number ofantennae, and so forth. As set forth in more detail below, each column(as a discrete unit) of candidate matrix, C, may be selected as acandidate vector for a respective column of the beamforming matrix;accordingly, it may not be necessary to compute each element of thebeamforming matrix, since each column is treated independently.

Selection of a transmit beamforming matrix may be executed at atransmitter (or “beamformer”), for instance, with knowledge of theforward channel which is generally available through feedback, orthrough sounding of the backward channel, assuming channel reciprocity.In many instances, even though channel reciprocity does not hold due toradio frequency (RF) chains and other factors, the forward channel maynevertheless be estimated from the backward channel estimate byexecuting various calibration techniques. Additionally or alternatively,the transmit beamforming matrix may be executed at the receiver (or“beamformee”), which generally has channel knowledge through sounding ofthe forward channel.

Whether the transmit beamforming matrix is selected at the transmitteror at the receiver, it may be assumed that the selection is informed byknowledge of both the channel, H, and the transmit beam candidatematrix, C, or with knowledge of the combined effective channel H_(e)ΔHC.

A special case of beamforming matrix selection arises when the transmitbeam candidate matrix, C, is given as an identity matrix, i.e.,C=I_(NT); this represents a situation in which the problem of matrixselection degenerates into simple selection of transmit antennas. Inthat regard, the methodologies set forth herein are general enough toaddress both the problem of transmit antenna selection as well as theproblem of transmit beamforming matrix selection as set forth in moredetail below.

With the transmit beamforming matrix, B, the model described above maybe expressed as follows (combining Equations 1 and 6):y=HBd+z  (Equation 8)

Given the relationship defined in Equation 8, it may be desirable toconstruct matrix, B, such that receiver performance may be maximized fora given receiver type. It will be appreciated that the best beamformingmatrix may generally depend upon, among other factors, the type andfunctionality of a multiple input, multiple output (MIMO) equalizeremployed by the beamformee. Examples of MIMO equalizers include, but arenot limited to: zero-forcing (ZF) linear equalizers (LEs); minimum meansquare error (MMSE) LEs; ZF decision feedback equalizers (DFEs); andMMSE DFEs. A maximum likelihood receiver may also be employed. In thefollowing example, it is assumed that the beamformee is implementing aZF linear equalizer, though the present disclosure is not intended to belimited by the nature or architectural and operational characteristicsof the equalizer utilized at the beamformee.

Transmit Beam Selection

FIGS. 2 and 3 are simplified flow diagrams illustrating operation ofembodiments of beamforming methods that select candidate vectors toconstruct a beamforming matrix. One example, illustrated in FIG. 2,involves a situation in which the number of candidates, N_(C), is lessthan or equal to the number of receive antennas, N_(R), such that therank of the transmit beam candidate matrix, C, is N_(C). Anotherexample, illustrated in FIG. 3, involves a situation in which the numberof candidates, N_(C), is greater than the number of receive antennas,N_(R).

As noted above, it may be desirable to select columns from the candidatematrix that construct a beamforming matrix suitable for a particularreceiver. In some embodiments, a greedy transmit beam selectionalgorithm may simply remove one column vector at a time, starting fromthe full effective channel matrix, H_(e)=HC. One criterion that may haveparticular utility for column removal is the substream SNR.

In accordance with the FIG. 2 embodiment, a method of transmit beamselection may begin with receiving a candidate matrix as indicated atblock 201. As set forth above, the candidate matrix may represent aseries of column vectors, each of which may represent a candidate columnto be used to construct the beamforming matrix. The candidate matrix maybe given, or predefined, and may be selected in accordance with desiredor required overall system constraints. As set forth above, thecandidate matrix may be an identity matrix in some implementations. Thecandidate matrix may be used to construct an effective channel matrix,H_(e) (e.g., by multiplying the candidate matrix with the instantaneouschannel matrix), as indicated at block 202.

Equalization may be performed as indicated at block 203. Suchequalization may be based on the effective channel matrix. It will beappreciated that, at least initially, all columns of C may be selectedfor the first iteration through the loop illustrated in FIG. 2, i.e.,initially, the dimensions of H_(e) will be N_(R)×N_(C). Many differenttypes of equalization techniques exist, and may be suitable for variousapplications. The equalization performed at block 203 may be executed inaccordance with the nature or operational characteristics of theequalizer employed by the beamformee, for instance. By way of example,in the case of ZF linear equalizers (which are commonly employed), a QRdecomposition algorithm may be executed, however, the present disclosureis not intended to be limited to any particular equalization technique.

As indicated at block 204, a respective substream SNR may be calculatedfor each of N_(T) beams, assuming that each of the other beams(represented by the respective columns of H_(e)) are present. As isgenerally known, SNR calculations may depend upon, among other factors,the equalization technique employed at block 203, i.e., the calculating(at block 204) may be executed responsive to the equalization (at block203). In some implementations, it may be desirable to remove the columnof H_(e) that corresponds to the beam having the lowest substream SNR asindicated at block 205. Having modified the matrix H_(e) by removing acolumn representing the beam with the lowest SNR, the process may loopback to block 203 (as indicated by the dashed arrow in FIG. 2) whereadditional equalization may be performed on the modified matrix.

In the foregoing manner, transmit beam selection may be greatlysimplified. The strategy illustrated in FIG. 2 may simply remove thebeam that has the smallest SNR based on the heuristic reasoning thatthis beam will probably have a small norm, will severely interfere withother beams, or both. This strategy avoids an exhaustive search forevery element in the beamforming matrix, and reduces attendantcomputational overhead.

Another advantage of this transmit beam selection strategy is that itdoes not require any additional mechanism or modification to existinghardware, other than implementing the selection and removal of the beamhaving the lowest SNR. In that regard, the receiver of the beamformeealready has a MIMO equalizer, and already has a capability ofcalculating substream SNR if the receiver does soft decoding. Thus, allthe beamformee needs to do for transmit beam selection is to calculatesubstream SNR values iteratively with a shrinking beamforming matrix (asdescribed above) and to select a beam having the lowest substream SNRfor elimination at each iteration.

Turning now to FIG. 3, it will be appreciated that in some instances thenumber of candidate beams, N_(C), may be greater than the number ofreceive antennas, N_(R). In this case, a method of transmit beamselection may also begin by receiving a candidate matrix at block 301;this operation may be substantially identical to that described withreference to block 201 in FIG. 2. The FIG. 3 embodiment may additionallyinclude limiting the candidate matrix to a predetermined number ofcolumns (e.g., selecting an initial N_(R) beams out of the N_(C)candidates) as indicated at block 302. In particular, it may bedesirable to select a set of N_(R) beams which exhibits the maximum sumof substream SNRs over all candidate beams. Alternatively, it may bedesirable to select a set of N_(R) beams which exhibits the maximum sumof substream SNRs over the largest N_(S) beams. By pre-selecting anumber of candidates equal to the number receive antennae, the algorithmdescribed above may be employed.

The FIG. 3 embodiment includes an equalization procedure including QRdecomposition (as indicated at block 304) though other equalizationtechniques may be employed depending, for example, upon thecharacteristics of the equalizer implemented at the receiver. In someembodiments, QR decomposition may be performed on H_(e)=QR, where H_(e)is the effective channel matrix constructed from the candidate matrix(block 303). In such instances, a respective substream SNR may becomputed for each beam (as indicated at block 305) based on the matrix,R. In that regard, it is noted that all necessary information on thechannel may be found in the matrix, R, such that the Q matrix may beignored. The column of R that corresponds to the stream having thelowest SNR may be removed (block 306), and the modified matrix may bedenoted as {tilde over (R)}₁. The iterative nature of the procedure isindicated by the dashed arrow back to block 304.

In implementations employing a ZF-LE, given the matrix R, the SNR of thei^(th) substream may be computed based on the Euclidean norm of the rowof the Pseudo-inverse of matrix R:

$\begin{matrix}{\eta_{i} = \frac{\rho}{N_{C}{r_{i}}^{2}}} & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$where ρ is the average receive pre-processing SNR at one receiveantenna, and r_(i) is the i^(th) row of the Peudo-inverse of matrix R.

In the simplest case of N_(c)=N_(R)=2, R may be expressed as

$\begin{matrix}{R = \begin{bmatrix}r_{11} & r_{12} \\\; & r_{22}\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 10} \right)\end{matrix}$and

$\begin{matrix}{{\eta_{1} = \frac{\rho}{2\left( {\frac{1}{r_{11}^{2}} + \frac{{r_{12}}^{2}}{r_{11}^{2}r_{22}^{2}}} \right)}};{\eta_{2} = \frac{\rho}{2\left( \frac{1}{r_{22}^{2}} \right)}}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

Therefore, antenna selection may be calculated by removing the columnfrom R with the index satisfying

$i_{RM} = {\underset{i}{\arg\;\min}{\eta_{i}.}}$The foregoing procedures are easily extendable for larger number ofchannel dimensions. Also, similar substream SNR expressions may bederived for other equalizer types such as MMSE-LE, ZF-DFE, and MMSE-DFE.

In particular, for i=2 to N_(T)−N_(S): a QR decomposition may beperformed on {tilde over (R)}_(i−1), with the new upper triangularmatrix being denoted R_(i); and the column of R_(i) that corresponds tothe beam having the lowest SNR may be removed, with the modified matrixbeing noted as {tilde over (R)}_(i). This algorithm may reduce thenumber of columns in the beamforming matrix to N_(S). The foregoingtechnique is simple to implement with receivers using ZF linearequalizers, and may readily be executed with existing hardware.

In many cases, QR decomposition may be achieved using Givens rotation.In that case, the QR decomposition on {tilde over (R)}_(i) is of lowcomplexity because the matrix is already very close to the uppertriangular matrix. For example, consider the case of N_(T)=4 with R₁ asfollows:

$\begin{matrix}{R_{1} = \begin{bmatrix}r_{11} & r_{12} & r_{13} & r_{14} \\0 & r_{22} & r_{23} & r_{24} \\0 & 0 & r_{33} & r_{34} \\0 & 0 & 0 & r_{44}\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 12} \right)\end{matrix}$

Assume that the beam that corresponds to the second column from the lefthas the lowest SNR. Then {tilde over (R)}₁ may be expressed as:

$\begin{matrix}{{\overset{\sim}{R}}_{1} = \begin{bmatrix}r_{11} & r_{13} & r_{14} \\0 & r_{23} & r_{24} \\0 & r_{33} & r_{34} \\0 & 0 & r_{44}\end{bmatrix}} & \left( {{Equation}\mspace{14mu} 13} \right)\end{matrix}$

With Givens rotation, only the elements r₂₃, r₃₃, r₃₄, and r₄₄ need tobe processed. In that regard, the Givens rotation need only be appliedto the diagonal elements and sub-diagonal elements in the columnslocated to the right of the column that has been removed. Furthermore,the processing on r₃₃ and r₄₄ will be simple because these elements arereal numbers.

Here, the QR decomposition approach may have particular utility, sinceit may be easily implemented by the COrdinate Rotation Digital Computer(CORDIC) algorithm, a hardware technology well-known in circuit designfor realizing Givens rotations. Therefore, powered by CORDIC algorithm,the proposed beam selection method set forth herein may be implementedby dedicated hardware (e.g., by a field programmable gate array (FPGA)or an ASIC) for true fast and real-time processing, although it may alsobe advantageous (regarding speed, delay, and other performancecharacteristics) for use in connection with conventional software DSPrealizations.

In sum, a greedy transmit beam selection algorithm may remove beams, oneby one, starting from the full effective channel matrix constructed fromthe full candidate matrix. At each iteration of the beam removalprocess, a column representing the beam that corresponds to the lowestSNR may be removed from the beamforming matrix. The disclosed system andmethod are appealing to the extent that they introduce minimal change toreceiver hardware, particularly with respect to receivers that employMIMO equalizers and have the capability to calculate substream SNRvalues. Even when beam selection is executed at the transmitter, thetransmitter usually has a receiver part and can reuse the receiver MIMOequalizer and substream SNR calculation unit for the transmit beamselection. As set forth above, an algorithm for ZF linear equalizers maybe based on QR decomposition. This strategy may be applied to manydifferent MIMO equalizers such as those implementing ZF-LE, MMSE-LE,ZF-DFE, and MMSE-DFE technologies. Finally, the disclosed transmit beamselection strategy may be directly applied to the transmit antennaselection problem given a particular candidate matrix.

Several features and aspects of the present invention have beenillustrated and described in detail with reference to particularembodiments by way of example only, and not by way of limitation. Thoseof skill in the art will appreciate that alternative implementations andvarious modifications to the disclosed embodiments are within the scopeand contemplation of the present disclosure. Therefore, it is intendedthat the invention be considered as limited only by the scope of theappended claims.

1. A method of constructing a beamforming matrix; said method comprising: receiving a candidate matrix; constructing an effective channel matrix using the candidate matrix; performing equalization on the effective channel matrix; calculating a respective signal to noise ratio for each beam in the effective channel matrix; responsive to said calculating, modifying the effective channel matrix by removing a column; and selectively repeating said performing equalization, said calculating, and said removing.
 2. The method of claim 1 wherein the candidate matrix is predefined.
 3. The method of claim 2 wherein the candidate matrix is an identity matrix.
 4. The method of claim 1 wherein said constructing comprises multiplying the candidate matrix with an instantaneous channel matrix.
 5. The method of claim 1 wherein said performing equalization is executed in accordance with characteristics of an equalizer employed at a receiver.
 6. The method of claim 5 wherein the equalizer is a linear equalizer and wherein said performing equalization comprises executing a QR decomposition technique.
 7. The method of claim 1 wherein said calculating is responsive to said performing equalization.
 8. The method of claim 1 wherein said removing comprises removing a column of the effective channel matrix corresponding to a beam having a lowest signal to noise ratio.
 9. The method of claim 1 further comprising limiting the candidate matrix to a predetermined number of columns.
 10. The method of claim 9 wherein said limiting comprises pre-selecting a number of columns in the candidate matrix equal to a number of antennae utilized by a receiver.
 11. A beamformer comprising: a beamforming matrix module to construct an effective channel matrix using a candidate matrix; an equalizer to perform equalization on the effective channel matrix; and a signal to noise calculation unit to calculate a respective signal to noise ratio for each beam in the equalized effective channel matrix; wherein said beamforming matrix module is to remove a column of the equalized effective channel matrix responsive to the calculated respective signal to noise ratios.
 12. The beamformer of claim 11 wherein the candidate matrix is predefined.
 13. The beamformer of claim 12 wherein the candidate matrix is an identity matrix.
 14. The beamformer of claim 11 wherein said beamforming matrix module multiplies the candidate matrix with an instantaneous channel matrix to construct the effective channel matrix.
 15. The beamformer of claim 11 wherein said equalizer performs equalization in accordance with characteristics of a beamformee equalizer employed at a receiver.
 16. The beamformer of claim 15 wherein said equalizer is a linear equalizer.
 17. The beamformer of claim 16 and wherein said equalizer executes a QR decomposition technique.
 18. The beamformer of claim 15 wherein said equalizer is a decision feedback equalizer.
 19. The beamformer of claim 11 wherein said beamforming matrix module is to remove a column of the equalized effective channel matrix corresponding to a beam having a lowest signal to noise ratio.
 20. A beamformer comprising an apparatus operative to perform the method of claim
 1. 